Which algorithm should I choose: An evolutionary algorithm portfolio approach

Many good evolutionary algorithms have been proposed in the past. However, frequently, the question arises that given a problem, one is at a loss of which algorithm to choose. In this paper, we propose a novel algorithm portfolio approach to address the above problem for single objective optimization. A portfolio of evolutionary algorithms is first formed. Covariance Matrix Adaptation Evolution Strategy (CMA-ES), History driven Evolutionary Algorithm (HdEA), Particle Swarm Optimization (PSO2011) and Self adaptive Differential Evolution (SaDE) are chosen as component algorithms. Each algorithm runs independently with no information exchange. At any point in time, the algorithm with the best predicted performance is run for one generation, after which the performance is predicted again. The best algorithm runs for the next generation, and the process goes on. In this way, algorithms switch automatically as a function of the computational budget. This novel algorithm is named Multiple Evolutionary Algorithm (MultiEA). The predictor we introduced has the nice property of being parameter-less, and algorithms switch automatically as a function of budget. The following contributions are made: (1) experimental results on 24 benchmark functions show that MultiEA outperforms (i) Multialgorithm Genetically Adaptive Method for Single Objective Optimization (AMALGAM-SO); (ii) Population-based Algorithm Portfolio (PAP); (iii) a multiple algorithm approach which chooses an algorithm randomly (RandEA); and (iv) a multiple algorithm approach which divides the computational budget evenly and execute all algorithms in parallel (ExhEA). This shows that it outperforms existing portfolio approaches and the predictor is functioning well. (2) Moreover, a neck to neck comparison of MultiEA with CMA-ES, HdEA, PSO2011, and SaDE is also made. Experimental results show that the performance of MultiEA is very competitive. In particular, MultiEA, being a portfolio algorithm, is sometimes even better than all its individual algorithms, and has more robust performance. (3) Furthermore, a positive synergic effect is discovered, namely, MultiEA can sometimes perform better than the sum of its individual EAs. This gives interesting insights into why an algorithm portfolio is a good approach. (4) It is found that MultiEA scales as well as the best algorithm in the portfolio. This suggests that MultiEA scales up nicely, which is a desirable algorithmic feature. (5) Finally, the performance of MultiEA is investigated on a real world problem. It is found that MultiEA can select the most suitable algorithm for the problem and is much better than choosing algorithms randomly.